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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 400710.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.l1 | 400710l2 | \([1, 1, 0, -161697, 24959301]\) | \(1295169456680034481/12156720\) | \(4388575920\) | \([]\) | \(1586304\) | \(1.4300\) | \(\Gamma_0(N)\)-optimal* |
400710.l2 | 400710l1 | \([1, 1, 0, -2097, 29781]\) | \(2827062172081/511488000\) | \(184647168000\) | \([]\) | \(528768\) | \(0.88071\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400710.l have rank \(1\).
Complex multiplication
The elliptic curves in class 400710.l do not have complex multiplication.Modular form 400710.2.a.l
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.